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The Golden ratio which appears in the geometry of a variety of creations in Nature is found to arise right in the Bohr radius of the hydrogen atom due to the opposite charges of the electron and proton. The bond length of the hydrogen molecule is the diagonal of a square on the Bohr radius and hence also has two Golden sections, which form the cationic and anionic radii of hydrogen. It is shown here that these radii account quantitatively for the bond lengths of many hydrides when added to the atomic and Golden ratio based ionic radii of many other atoms.

Golden sections of inter-atomic distances as exact ionic radii of atoms